An Improved Constrained LMS Algorithm for Fast Adaptive Beamforming Based on a Low Rank Approximation

Adaptive beamformers use data from sensor arrays to capture signal from a desired direction without any distortion, in the presence of interfering signals from other directions in a noisy environment. Most beamformers achieve this goal by minimizing their variance while applying distortionless and null constraints in the direction of the desired and interfering signals, respectively. Constrained least-mean-square (CLMS) algorithms have been developed to iteratively update the weights of such beamformers. In this brief, we propose a novel and improved CLMS beamforming algorithm based on a low rank approximation technique called the nearest Kronecker product decomposition. By decomposing the weight vector into a sequence of Kronecker products of smaller vectors, the original weight update process is converted into updates of smaller vectors. The decomposition allows us to control the trade-off between steady-state performance and faster convergence based on the rank of the beamforming system. We derive the update rules of the proposed algorithm, tabulate its computational complexity and perform simulation study to show its superiority.